Question

if x+y+z=0 then show that x3+ y3+z3=3xyz​

Answer 1

x³ + y³ + z³ - 3xyz = ( x + y + z ) ( x² + y² + z² + xy + yz + zx )

❥ Given :- x + y + z = 0

x³ + y³ + z³ - 3xyz = 0 ( x² + y² + z² + xy + yz + zx )

Any number multipled by 0 is 0 .

x³ + y³ + z³ - 3xyz = 0

So , x³ + y³ + z³ = 3xyz

Hence proved

Answer 2

Answer:

x³+y³+z³-3xyz=(x+y+z)(x²+y²+z²-xy-yz-xz)

=(0)(x²+y²+z²-xy-yz-xz)

x³+y³+z³-3xyz=0

x³+y³+z³=3xyz